R Hansen says:>This is written as if people (in general, uneducated or not) actively and *thoughtfully* compress number scales. They do nothing of the sort. In fact, even when you explain the connection between these number scales and the math behind them, the majority still do not understand, even a smidgen, yet they can use the principle in conversation just fine.

This reminds me of the conversation weeks ago about logic.I quoted the Stanford Encyclopedia of Philosophy as saying something (approx) that logic begins with the "reflected" use of commonly employed language patterns. You had some objection to that I believe. I think the connection between logic and what "comes naturally" is even more clear and compelling than the case with mathematics in general, but its a close analog.

If a person can be taught that the log(10) of 100 is 2, and 1000 is 3, and so on, do they know a smidgen?